. The Philosophical magazine; a journal of theoretical, experimental and applied physics . hore along which the solution shows a slope of more than\ is only a small fraction of a millimetre. Thus this depar-ture from reality is of no importance whatever. When 0=0 or +7r, being + when 6=0, and — when d=±7r. When 0= ±^7r, a. vanishes; and therefore midway in theocean and on the land there are nodal lines, which alwaysremain in the undisturbed surface, when the tide rises andfalls. At these nodal lines, defined by 0= ±^77, da ,, .0-2/1 11 ) = +-6168=-•9634 and +-2702. Thus the slope is gre
. The Philosophical magazine; a journal of theoretical, experimental and applied physics . hore along which the solution shows a slope of more than\ is only a small fraction of a millimetre. Thus this depar-ture from reality is of no importance whatever. When 0=0 or +7r, being + when 6=0, and — when d=±7r. When 0= ±^7r, a. vanishes; and therefore midway in theocean and on the land there are nodal lines, which alwaysremain in the undisturbed surface, when the tide rises andfalls. At these nodal lines, defined by 0= ±^77, da ,, .0-2/1 11 ) = +-6168=-•9634 and +-2702. Thus the slope is greater at mid-ocean than at assuming 6 successively as ^tt, I-tt,-^tt, and summingarithmetically the strange series which arise, we can, on pay- dtie to Elasticity of the Earths Surface. 419 ing attention to the manner in which the signs of the seriesoccur, obtain the values of a corresponding to 0, ±^7r, +^7r,±6 7, ±§7, ±^7r, +^7r, +§7r. The resulting values,together with the slopes as obtained above, are amply suffi-ient for drawing a figure, as shown The straight line is a section of the undisturbed level, theshaded part being land, and the dotted sea. The curve showsthe distortion, when warped bj high and low tide as indicated. The scale of the figure is a quarter of an inch to ^tt for theabscissas, and a quarter of an inch to unity for the ordinates;it is of course an enormous exaggeration of the flexure actu-ally possibly due to tides. It is interesting to note that the land-regions remain verynearly flat,*rotating about the nodal line, but with slight cur-vature near the coasts. It is this curvature, scarcely percep-tible in the figure, ^shich is of most interest for practicalapplication. The series (8) and (9) are not convenient for practical cal-culation in the neighbourhood of the coast, and they must bereduced to other forms. It is easy, by writing the cosines intheir exponential form, to show that cos0 + icos2^ + ^cos36 + ...= -log,
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